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Automatic Burst Detection
The goal of this survey is to automatically identify a burst in a spike train. Bursts are considered as a unit of neural information since they denote a period of 'high activity' in a given spike train. A generally accepted, rough definition of a burst is "an occurence of "many" spikes in a "small" time interval" 1 Most neurons can burst if stimulated or manipulated pharmacologically. Much research has been focused on the way that a neuron fires an individual spike or burst (for example see link 1). This study however will not focus on the how part of the process but will rather attempt to detect burst activity by examining the output ie the spike train. We will review some methods that are commonly used and also test them in a set of computer-generated data inspired from 2. The problem is set like this: given a spike train that may contain a number of bursts, find the same bursts that would be identified by an "expert" upon visual inspection. Introduction, some measures of activity and a global approach to the problem From a signal processing point of view, we must first describe an appropriate measure of the interesting activity. This measure should be able to cover the intuitive definition of a burst that we already stated. For example, a simple approach would be to compare the firing frequency of a period of spontaneous neuron activity with another, candidate period of bursting activity. Another simple approach would be to use the distribution of the interspike intervals (ISIs) during a time period. Such measures can be used to compare two different time periods of activity. Thus, if we are provided with a spike train of a neuron's spontaneous activity we can use the selected measure to denote if another spike train displays significant activity. *Example 1 : Consider the spike train in figures 1&2. One can easily say that this neuron displays a period of intense activity between 2200 and 2800 ms. For this example, we arbitrarily set three different epochs of activity: the first one between 0 and 2000 ms the second between 2000 and 3000ms and the third between 3000 and 4000ms. Figure 1 shows the firing rate of the spike train. The following table displays the average firing rate of each epoch. The firing rate of the second epoch is sufficiently higher than the mean firing rate of all the other epochs and we can conclude that epoch two is a period of higher bursting activity. Figure 2 shows the ISIs distribution for the different epochs. Notice the peak at © that denotes many short interspike intervals and a possible burst period. A small peak at medium-sized intervals can be seen at (b) whereas (d) has no significant peaks. The histogram at (e) has two peaks: one corresponding to short inerspike intervals (coming from the second epoch) and one corresponding to medium-sized intervals (coming from the other non-bursting epochs. Assuming that we have a suitable measure to compare two periods of neuron activity and that we are provided with a period of spontaneous activity we can proceed to the second part of our approach. The problem now is to find a period in the spike train that maximizes the measure of difference when compared with the spontaneous activity. A simple but effective approach would be to estimate our measure at all the possible time intervals and denote as burst the one with the maximum difference. If we expect to find multiple bursts, we can use a threshold to find time intervals that significantly differ from the given spontaneous period. Additional constrains can also be applied, such as that a burst must have a minimum or maximum number of spikes or that a burst can't be longer or shorter than a given time constant. Conclusively, a general outline to burst detection would consist of two parts: *(One) Find an appropriate measure that will be used to compare two periods of spike activity *(Two) Find the period in the given spike train that differs significantly from a period of spontaneous activity by using the measure described in (One) All the methods that will be described next share this common outline. The Poisson Surprise *Description The poisson surprise is a somewhat widely used method for burst detection. It is based on the assumption that neuron firing follows a poisson process or, in other words, that the interspike intervals (ISIs) distribution is a poisson distribution. This assumption comes from the analysis of Smith & Smith in 1965 3. The poisson surprise method was first described by Legendy & Salcman 4. Since then, various modifications of the algorithm have been used. They all follow the same principles that we will briefly describe next. The poisson probability distribution function is given by P \tau,k = \frac{e^{-\lambda \tau} (\lambda \tau)^k}{k!} \qquad k= 0,1,\ldots, . Here, P is the probability that k events occur in the time interval \tau . The parameter \lambda is the mean of the distribution. In the case of a spike train, if the assumption is valid, \lambda can be set as the mean firing rate. Thus, \lambda = \frac{N} {duration} , where N is the number of spikes in the train or \lambda = \frac{1}{mean(ISI)} . The Poisson surprise method constists of two major components : 1)i am beautiful 2)I am suprised by a poisson manner of my beautifullness *Pros *Cons *To Do The Rank Surprise *Description *Pros *Cons *To Do Cumulative histograms over trials *Description *Pros *Cons *To Do Mean firing rate *Description *Pros *Cons *To Do Significance sliding window See also *Izhikevich E. M. (2006) Bursting. Scholarpedia, p.1401. References 1 Palm G. Evidence, information and surprise. Biol Cybern 1981; 42(1):57-68 2 Raos V, Umilta MA, Murata A, Fogassi L and Gallese V. (2006) Functional properties of grasping-related neurons in the ventral premotor area F5 of the macaque monkey. J Neurophysiol, 95:709-29 3 Smith, D. R. & Smith, G. K. A statistical analysis of the continual activity of single cortical neurones of the cat unanaesthetized isolated forebrain. Biophys. J. 5: 47-74, 1965. 4 Legendy CR, Salcman M. Bursts and recurrences of bursts in the spike trains of spontaneously active striate cortex neurons. J Neurophysiol 1985;53(4): 926–39.